If at all possible, try to work with the OC. If they still own the debt see if you can pay them and they recall the debt from the CA. This will remove the collection from the CR.
The newer the collection, the more impact it has on your score. The older, less impact.
Paying off a collection should never hurt your score. Also, FICO looks at paid and unpaid collections the same. The only way to improve the score would be to have them removed.
It's not generally a good idea to try and get credit within 6 months of purchasing a house. You will have inquiries added to your CR and if you are approved, any new TL will temporarily drop your score. It will go back up quickly though.
A friend just closed on an FHA loan with BOA and she had 4 medical collections when she applied for the loan.